Scale Navigator

Slide from Planck (10−35m) to cosmic (1026m) and see how γ changes at every scale. The claim is that one equation applies at every scale — see the epistemic-status note below for what has and hasn't been tested.

Epistemic status of this table (2026-06-08 audit): Every Ncorr value in this navigator is asserted, not independently measured. No counting protocol exists that derives Ncorr from a Hamiltonian without first fitting γ to observed data — so the displayed Ncorr values are back-computed from γ, not forward-predicted from physics. Only ~4 of 17 rungs have ever been confronted with data; all fail or are null. The galaxy rung is self-contradictory in both directions: the framework asserts Ncorr=1 (independent stars) → γ=2, but SPARC RAR rejects γ=2 (ΔBIC=+184); the data-preferred γ≈0.49 back-implies Ncorr≈17 — contradicting the independent-stars premise that motivates applying C(ρ) to galaxies at all.

Neural network

Brain

10-2 m

Ncorr

10⁹

γ

~10⁻⁵

Consciousness threshold C ≈ 0.50. Massive correlated firing.

10⁻³⁵m10²⁶mγ ≈ 1

The claim: the same equation C(ρ) = tanh(γ · ln(ρ/ρcrit + 1)) applies at every one of these scales. One function, 80 orders of magnitude, from Planck to cosmic. Whether that claim survives testing is what the top 5 tests are for.

Galaxy Scale: γ = 2 is asserted and rejected

The framework asserts stars are uncorrelated (Ncorr = 1, γ = 2), the same γ as an ideal gas, and applies C(ρ) at this value to predict rotation curves. However, γ=2 is rejected on SPARC RAR at ΔBIC=+184 (conservative threshold ≥33) — the data-preferred free γ≈0.49 equals MOND. Furthermore, γ≈0.49 back-implies Ncorr≈17 (“stars correlated in units of ~17”), directly contradicting the Ncorr=1 independent-stars premise.

All Scales at a Glance

ScaleSystemNcorrγ
10-35mPlanck length12
10-15mNucleus31.15
10-10mAtom12
10-9mMolecule41
10-8mProtein500.28
10-7mVirus2000.14
10-6mBacterium10000.06
10-5mCell100000.02
10-2mBrain10⁹~10⁻⁵
100mHuman10²³~10⁻¹²
107mEarth10⁵⁰~10⁻²⁵
1013mSolar system10⁵⁷~10⁻²⁹
1018mGalaxy arm12
1021mGalaxy12
1023mGalaxy cluster12
1026mObservable universe12

Related Concepts

Scale InvarianceFrom Planck to cosmic: 80 orders of magnitudeThe γ Parameterγ = 2/√N_corr: why 2, why √N